Substitute both these in the original equation. 4 does not satisfy the original equation, but 16 does.
Therefore, the only solution is 16.
Verify that (2x-7) is positive for both values of x. It is.
Therefore, the solutions are 4 and 16.
Now why did we get 4 as a possible answer? Because of the very first step - we squared both sides.
If you look at the left hand side when x = 4, you see it evaluates to -1. The square of -1 is the same as the square of 1. That is why 4 was a possible answer of the SQUARED equation, but not of the original equation!
Answers & Comments
Verified answer
√(2x-7) - √x = 1
Square both sides
2x - 7 + x -2√(2x^2-7x) = 1
3x -8 = 2√(2x^2-7x)
Square both sides
9x^2 - 48x + 64 = 4(2x^2-7x) = 8x^2 - 28x
x^2 - 20x + 64 = 0
(x - 16)(x - 4) = 0, x can be 16 or 4
Substitute both these in the original equation. 4 does not satisfy the original equation, but 16 does.
Therefore, the only solution is 16.
Verify that (2x-7) is positive for both values of x. It is.
Therefore, the solutions are 4 and 16.
Now why did we get 4 as a possible answer? Because of the very first step - we squared both sides.
If you look at the left hand side when x = 4, you see it evaluates to -1. The square of -1 is the same as the square of 1. That is why 4 was a possible answer of the SQUARED equation, but not of the original equation!
If you mean â(2x - 7) - âx = 1 then do this:
square both sides:
(2x - 7) - 2[â(2x - 7) * âx] + x = 1
2x - 7 - 2â[(2x - 7)x] + x = 1
3x - 7 - 2â(2x² - 7x) = 1
3x - 8 = 2â(2x² - 7x)
Square both sides again:
9x² - 48x + 64 = 4(2x² - 7x)
9x² - 48x + 64 = 8x² - 28x
x² - 20x + 64 = 0
Factoring ... or you could use the quadratic formula to solve:
(x - 4)(x - 16) = 0
x - 4 = 0 or x - 16 = 0
x = 4 or x = 16
Now b/c squaring was used as part of the solution have to check for false answers:
when x = 4 â â(8 - 7) - â4 = 1 - 2 = -1 ... NOT 1 ... so reject x = 4
when x = 16 â â(32 - 7) - â16 = 5 - 4 = 1 ... TRUE
so the only solution is x = 16